Frequency sensitive circuit



June 1949- L. E. MATSON, JR, ETAL 2,472,167

FREQUENCY SENSITIVE CIRCUIT Filed March 1,3, 1945 k E g wb 3 V; 4

w i i r I mmuz/vcr E 2 H 7 INV EN T 0R8 Lew/ e E. M21700 :71:-

Meg 4 ATTORNEY.

Patented June 7, 1949 FREQUENCY SENSITIVE CIRCUIT Leslie E. Maison, Jr.,Collingswood, and Robert N. Lesnick, Camden, N. J., assignors to RadioCorporation of America, a corporation of Dela 'ware Application March13, 1945, Serial No. 582,540

8 Claims.

This invention relates to frequency sensitive circuits, and its primeobject is to provide a simple, compact and inexpensive circuit foradding to an amplitude modulated signal a component representative ofthe rate of change of the modulation of the signal.

It is sometimes undesirable to introduce inductive elements intofrequency responsive circuits, particularly when signals of low frequencare concerned, because inductors are bulky and expensive by comparisonwith other reactors and because magnetic interaction may occur betweenthe inductors and other electrical elements.

It is, therefore, an object of the invention to provide an improvedfrequency responsive circuit containing resistive and capacitiveelements only.

A circuit of the character described may have many applications in theelectrical arts. One such application is in electrical control systemsof the type in which there is produced an alternating signalrepresentative of a condition to be controlled by the system. To avoidhunting due to inertia and the like, and thus to stabilize the operationof the system, it is desirable to introduce in the control signal acomponent representative of the rate of change of its amplitude or,inthe case of a servo or follow-up system, of the rate of change ofposition.

It is, therefore, an object of the invention to provide an improvedmethod of and means for stabilizing an electrical control system.

An additional object is to provide an improved anti-hunting arrangementin a system of the character described.

A further object is to provide an improved method of and means forintroducing a velocity component in the control signal of an electricalcontrol system.

According to the invention these objects are achieved by providing twoparallel paths for a signal applied thereto. One of these pathsconstitutes a T-network having resistive series arms and a capacitiveshunt arm, while the other path constitutes another T-network havingcapacitive series arms and a resistive shunt arm. The values of theelements of the series arms are related to a particular frequency of theapplied signal, and the shunt arms are related in value to the seriesarms in a manner hereinafter described.

A permissible analysis is to regard one of the two networks as advancingthe phase of the applied signal while the other network retards thephase of the signal applied thereto. The impedances of the respectivenetworks also var the relative magnitude of the phasedisplaced signalsin each path. The combined output of the two paths comprises twocomponents which are, respectively, in phase with the input and 90 outof phase therewith. The in-phase component remains substantiallyconstant through a predetermined frequency range of the input, while theoutput component in quadrature with the input varies substantiallylinearly with the frequency of the applied signal through that range.The magnitude of the output varies with the magnitude of the inputsignal and also with the rate of change of magnitude of that signal. Aswill be later explained, suitable choice of the elements of the shuntarms determines the ratio in which these ingredients are present in theoutput.

The invention may be better understood from the following description oftwo embodiments thereof, when read in conjunction with the accompanyingdrawing in which:

Figure 1 is a diagram of an electrical control system including acircuit according to the invention,

Figure 2 is a circuit diagram of an alternative embodiment of theinvention, and

Figure 3 is a graph showing the frequency re-' sponse of the circuit ofthe invention.

Fig. l is a diagrammatic representation of a control system of the typeknown as a "followup or servo system. The system includes an input shaftl0 rotatable, as for example, by a crank 12 or by any other appropriatemeans and mechanically connected to the rotor winding I4 of a synchro orSelsyn element I 6. An output shaft IB'driven by an electric motor 20 iscon- I nected to a load 22 and also to the rotor winding 24 of anothersynchro element '26. The stator windings 28 and 30, respectively, of thetwo synchro elements are connected together as shown, and the synchroelements are connected to a source of alternating voltage indicated at32, which may, by way of example, be the commercial supply having afrequency of 60 cycles per second.

When thereis any difference between the angular positions of the inputand output shafts, an alternating voltage is generated in the rotorwinding of the synchro element l6. The magnitude of this voltage isproportional to the angular displacement between the two shafts and itsinstantaneous polarity depends upon which of the shafts leads or lagsthe other. Disregarding temporarily the circuit'34, the alternatingcontrol signal is applied to an amplifier 36 which may include a powercontrol circuit. The

signal thus obtained controls the speed and direction of rotation of thearmature of the motor 20. The motor drives the output shaft intopositional agreement with the input shaft by which time the controlsignal has been reduced to zero and the motor is de-energized.

Because of the inertia of the load 22 and other rotating parts of thesystem, and for other reasons, the shaft I8 and the load 22 may tend torotate in either direction about the point of agreement with the inputshaft, although the motor 20 has been deenergized. This effect is knownas hunting and reduces the stability of the system.

The basic frequency of the control signal is that of the power supply.However, as the angular disagreement between the two shafts varies, themagnitude of the control signal varies also. The control signal may beregarded as having a carrier frequency determined by the A. C. powersupply and as being modulated by a signal representative of thedisplacement between the input and output shafts of the system. Amodulated control signal of this type may be considered to be composedof a carrier and sidebands. In a common case, where the carrierfrequency is 60 cycles per second, the control signal may havecomponents in the range of, say, 55 to 65 cycles per second.

The magnitude of the control signal represents the displacement inposition between the input and output of the system. The addition to thecontrol signal of a velocity component, that is to say, of a componentrepresentative of the rate of change of that displacement, makes thecombined signal anticipatory of such changes. It therefore tends toreduce hunting and to improve the stability of the system. It is,therefore, desirable, to add to the control signal a componentrepresentative of the rate of change of the position between the inputand output of the servo system.

The circuit 34 is connected between the synchro element l6 and theamplifier 36, and consists of two T-networks connected in parallel witheach other. The circuit has an input terminal 38, an output terminal M,and a third terminal 42 common to input and output. One of theT-networks consists of two equal resistors M and 4'5 connected in seriesbetween the input and output terminals, and a capacitor 38 connected inshunt between the junction point of the two series resistors and thecommon terminal 42. The other T-network comprises two equal capacitors50 and 52 connected in series between the input and output terminals,and a resistor connected in shuntrbetween the junction point of the twoseries capacitors and the common terminal.

Each of the series resistors has a value of R ohms and. each of theseries capacitors of C farads. If we be taken as the radian frequency ofthe carrier signal, that is, of the control signal when the displacementbetween the input and output shafts is constant, then R and C are chosento satisfy the expression As before explained, one of the T-networksadvances the phase of the control signal and the other retards it. Ifthe shunt capacitor were chosen of a value of 2C farads and the shuntresistor of ohms, the phase shift attributable to each network would bebut in opposite directions in each case. The respective outputs of eachnetwork would then be in opposite phase, and maximum attenuation of thecarrier signal would be effected. The combined output of circuit 34would then be representative of the rate of change of the amplitude ofthe control signal, that is, of the rate of change of the positionaldifference between the shafts I0 and 18. It would contain no componentrepresentative of that difference itself.

The shunt capacitor 48, therefore, is given a value of farads and theresistor 54 a value of ohms, where q is equal to a positive numbergreater than zero. This has the effect of varying the relative magnitudeand phase of the outputs of the two T-networks. Within a given range offrequencies of the input to circuit 34, the component of its outputwhich is in phase with that input remains substantially constant, whilethe component which is 90 out of phase with the input varies linearlywith frequency. Thecombined output of the circuit contains a componentrepresentative of the displacement between the two shafts l0 and I8, andanother component representative of the rate of change of thatdisplacement.

The ratio of what may be described as the displacement component to thedisplacement rate component depends on the value of q. For the range offrequencies met with in some practical types of servo systems, a valuefor q of the order of -.2 has been found satisfactory.

Without entering into a detailed mathematical analysis of the operationof the circuit, the outut voltage e at any radian frequency w for unitinput voltage is defined by the expression 1+q where x= The approximateresponse of the circuit is illustrated by the curve of Fig, 3. At thecarrier frequency, the output of circuit 34 is a minimum but is still afinite value. When the carrier Signal is modulated and the frequency ofthe input varies about this point, the output increases and its phasewith respect to the input varies also. When the output leads or lags theinput by approximately 45, the output is /2 times that at the minimum.The ratio an of the band width between these two points to the carrierfrequency is a special case of :c, and is then approximately equal to q.

The circuit of the invention has been found to give a linear response tosignals which vary in frequency by 25 per cent from the frequency of thecarrier signal.

Since the value of q determines the proportion of the displacement ratecomponent in the signal applied by circuit 34 to amplifier 36, it may insome cases be desirable to vary the values of the shunt capacitor 48 andresistor 54. In that event, it may be desirable to employ thearrangement illustrated in Fig. 2. A variable resistor 56 is connectedin series with the fixed resister 54 and a variable capacitor 58 isconnected in parallel with the fixed capacitor N. The two variableelements are ganged and so arranged that by the operation of a singlecontrol the shunt resistance is increased while the shunt capacitance isdecreased to a like extent.

By connecting two or more circuits of the invention in series, it ispossible to introduce into the original signals componentsrepresentative of the second and higher order derivatives of thefrequency of the control signals.

Although the series resistors 44 and 46 and the series capacitors 50 and52 have been described as equal to each other respectively, thislimitation is inserted only because it is then easier to evaluate theresponse of the circuit. The characteristics of the circuit do notchange materially if the resistance of the two series arms in onenetwork, or the capacitance of the two series arms in the other network,are not equal.

There has thus been described a circuit comprising two T-networksconnected in parallel, one

network having series resistive branches and a shunt capacitive branch,and the other network having series capacitive branches and a shuntresistive branch. The values of the elements in the series branches arerelated to a given fre-- quency of the signal to be applied to thecircuit,

and the values of the elements in the shunt branches are related tothose in the series branches to add to' the original signal a componentrepresentative of the rate of change of its amplitude. By connectingsuch a circuit in the control signal path of an electrical controlsystem,'hunting of the output of the system may be reduced and asubstantial improvement in stability'secured. 1

While the invention has been described with particular reference to itsapplication to the control system illustrated in Fig. 1, it will beobserved that it may be used in many other connections wherever itisdesired (a) to add alge braically to a modulated alternating signal acomponent representative of the rate of change of its modulation, or (b)to add algebraically to a signal representing a given condition (forexample, a given amount of light passing to a lightsensitive element) acomponent representing the rate of change of that condition, or (c) toderive from a signal, which varies in frequency through a given,range,'a second signal having a substantially constant component inphase with the original signal and a component 90 out of phase with theoriginal signal, which varies linearly with the frequency of theoriginal signal.

We claim as our invention:

1. A frequency sensitive circuit comprising a T-network having twosubstantially equal seriesconnected resistors and a shunt capacitor, anda second T-network connected in parallel with the first and having twosubstantially equal series connected capacitors and a shunt resistor,said shunt capacitor and resistor having respective values of farads andohms, where C equals the capacitance in farads of each of theseries-connected capacitors, R: equals the resistance in ohms of each ofthe seriesconnected resistors, and q equals a positive number greaterthan zero.

2. A circuit according to claim 1, wherein q is series-connectedresistors and the other terminal connected to the common input-outputterminal,

and a resistor having one terminal connected to the junction point ofsaid series-connected capacitors and the other terminal connected tosaid common terminal, said last-mentioned capacitor and resistor havingrespective values of farads and ohms, where C equals the capacitance infarads of each of the series-connected capacitors, R equals theresistance in ohms of each of the series-connected resistors, and qequals a positive number greater than zero.

4. A circuit for adding to a modulated carrier wherein we equals saidcarrier frequency in radians per second, R equals the value of each ofsaid resistors in ohmsand C equals the value of each' of said capacitorsin farads, and said shunt capacitor and resistor having values of 1 +qfarads and ohms respectively, q being any positive number greater thanzero.

5. A circuit for adding to a modulated carrier signal a componentrepresentative of the rate of change of modulation of said signal,saidcircuit comprising a T-network having two substantially equalserially-connected resistors and a shunt capacitor, a second T-networkconnected in parallel with the first and having two substantially equalserially-connected capacitors and a shunt resistor, the value of saidserially-connected resistors and capacitors being related to thefrequency of the unmodulated carrier signal by the expression wherein weis the frequency of the unmodulated carrier signal in radians persecond, It equals Jar-ads and 7 the value of each of said resistors inohms and C equals the value of each or said capacitors in Iarads, andsaid shunt capacitor and resistor hav ing values or iaradsand ohms,where C equals the capacitance in farads of each of the series-connectedcapacitors, R. equals the resistance in ohms of each of theseriesconnected resistors, and q equals a positive number greater thanzero.

7. The combination, in an electrical control system with means forproducing alternating control signals representative of a condition tobe controlled by said system, of a frequency sensitive circuitcomprising a T-network having two substantially equal series-connectedresistors and a shunt capacitor, and a second T-network connected inparallel with the first and having two substantiallyv equal seriesconnected capacitors I and a shunt resistor, said shunt capacitor andresistor having respectivevalues of farads and ohms, where C equals thecapacitance in farads or each of the series-connected capacitors, Requals the resistance in ohms of each of the series-connected resistors,and q equals a positive number greater than zero.

8. The combination, in an electrical control system with means forproducing alternating control signals representative of a condition tobe controlled by said system, of a frequency sensitive circuitcomprising a network of resistive and capacitive elements only connectedin series with said control-signal-producing means, said network and thevalues of the elements being chosen to make said network the equivalentof two T-networks in parallel, the first having two substantially equalserially-connected resistors and a shunt capacitor, and said secondT-network having two substantially equal series-connected capacitors anda shunt resistor, said shunt capacitor and resistor having respectivevalues of REFERENCES CITED The following references are of record in thefile of this patent:

UNITED STATES PATENTS Number Name Date 2,088,654 Hull Aug. 3, 19372,093,665 Tellegen Sept. 21, 1937 2,206,695 Guanella July 2, 19402,233,415 Hull Mar. 4, 1941 2,354,141 Purington July 18, 1944 2,446,567White et al A g. 10, 1948

